This paper considers a class of aggregative congestion games with uncertain coupling constraints, and devises a distributed algorithm to seek the robust generalized Wardrop equilibrium (RGWE) under worst-case uncertainty. Utilizing robust optimization theory, we reformulate the original aggregative congestion game with uncertainty into a tractable and deterministic augmented problem. Building upon this reformulation, we design a fully distributed algorithm to seek the RGWE by integrating a projected primal-dual scheme and a dynamic tracking technique. The convergence of the proposed algorithm is rigorously guaranteed via singular perturbation theory and LaSalle's invariance principle. Furthermore, we explicitly characterize the relationship between the obtained RGWE and the robust generalized Nash equilibrium, as the latter captures full strategic interactions. Finally, numerical simulations on the charging control of plug-in electric vehicles corroborate our theoretical findings.

翻译：本文考虑一类具有不确定耦合约束的聚合拥塞博弈，并设计了一种分布式算法，在最坏情况不确定性下寻求鲁棒广义沃德罗普均衡（RGWE）。利用鲁棒优化理论，我们将原始含不确定性的聚合拥塞博弈重新表述为一个可处理且确定性的增广问题。基于该重新表述，我们通过集成投影原始-对偶方案与动态跟踪技术，设计了一种全分布式算法来求解RGWE。借助奇异摄动理论和拉萨尔不变性原理，所提算法的收敛性得到了严格保证。此外，我们明确刻画了所得RGWE与鲁棒广义纳什均衡之间的关系，后者捕捉了完整的策略交互。最后，针对插电式电动汽车充电控制的数值模拟验证了我们的理论结果。